In economics of all new products put on the market 90 fail a

In economics, of all new products put on the market, 90% fail and are taken off the market within three years. Using normal approximation for this binomial distribution without correction for continuity; if a store introduces 70 new products, what is the probability that fewer than 67 fail within the first three years?

Give answer accurate to three decimals; that is, for 0.12345 or 12.345%, give 0.1235.

Solution

Given n=70, p=0.9
mean=n*p=70*0.9=63
s=n*p*(1-p)

=sqrt(70*0.9*0.1)

= 2.51

So the probability is

P(X>57)

=P(X>56.5) (by using continouse corretion)

=P((X-mean)/s >(56.5-63)/sqrt(70*0.9*0.1))

=P(Z>-2.59)

= 0.9952 (check standard normal table)